Bases are the most important asset that you, as commander of X-Com, could ever possess. Bases are where you store your extra weapons and armor for your troops. It's where you store your ammunition, your captured aliens, your artifacts that you stole from the alien's ships and carcasses. It's where you fix those ships that were damaged in the battles with the alien space ships, and where you research these new and deadly forms of warfare. This is where you construct monstrous ships of awe-inspiring power and create armor of startling strength.
Bases come in many different shapes and forms. Some can be high rise buildings while others can be low slums. This doesn't impact you too much, though the higher the building, the larger a target it is for the alien ships to come in and blow holes in it until it's nothing but rubble and all your troops inside it are dead. The layout is that which you should count on the most. Bases with large layouts are able to have more items constructed in them, and can make good all-purpose bases. Bases with limited or contorted space needs to be specialized as a specific type of base, such as one which only repairs your vehicles, or only researches quantum physics, or only contains workshops. Don't neglect to put in a few living quarters and storage modules, though. If you are ever attacked by an organization, you will want at least a few soldiers on hand to take care of the pests. Also, if you are blitzing on Workshops, you should be aware that you will need storage modules in order to "store" the items which you just manufactured. I tend to buy as many bases as possible and specialize each one, usually dedicating one or two to vehicle repairs, one to quantum physics research, one to biochemistry, a few to housing my soldiers, and then one to three for housing workshops. I then create enough living quarters for at least one soldier in each base.
When planning your base, it should be noted that Vehicle Bays and Access Lifts are able to be infiltrated by insurgents. If your bases ever come under attack, these are the areas where the enemy will most likely enter from. To counter this, I usually cordon off these sections with a small string of Security Stations, be they the advanced or regular form. This usually means that the enemy is shredded before you even run into them, and, in case your defenses fall, you can be certain that they enemy will be down most of its assault force.
Finally remember that you can transfer people between stations. If you stick all your scientists and men in one base, it is very likely that one well-placed missile or beam can completely annihilate your entire platoon of troops and all your researchers, which is generally BAD. Also, you will only lose the men in your base if a piece of building falls on top of the bay through which your men enter and leave via car. Otherwise, the aliens can destroy your entire base and you'll be fine.